Polish-born Lukas Podolski celebrated his 100th appearance for Germany with his 44th international goal to put his side in front and although Michael Krohn-Dehli's equaliser gave the Danes hope of reaching the quarter-finals, Lars Bender struck 10 minutes from time to seal a third German victory in a row.
Germany will face surprise quarter-finalists Greece in Gdansk on Friday and Denmark, despite giving a good account of themselves in the tournament, go home.
Portugal finished runners-up in the tournament's toughest group after coming from behind to beat the Netherlands 2-1.
Despite only needing a point to guarantee reaching the last eight, Joachim Loew's powerful Germany side were never going to settle for a draw and produced another efficient performance full of positive, forceful football.
They have won 14 consecutive competitive matches since losing to Spain in the 2010 World Cup semi-finals.
While Podolski crept up the all-time list of Germany's scoring charts at the European Championship, moving joint third with Juergen Klinsmann on 15, Bender celebrated his first on his first start, clipping the ball into the corner of the net after 80 minutes.
"The most important thing is that we won," said 27-year-old Podolksi who smashed a shot past Danish goalkeeper Stephan Andersen after 19 minutes from a cross by Thomas Muller.
"It was a tough match against a strong Denmark team and fortunately we got the second goal and won it," Podolski added.
"It was something special for me that I got a goal in the 100th match and shot it with my right foot too."
GERMANY DOMINATED
Germany dominated the opening exchanges, seizing the initiative and creating several early chances, the best of which fell to an unmarked Muller who should have scored but his scuffed close-range shot was clutched on the line by a grateful Andersen.
Mario Gomez, who had overshadowed Podolksi in the two previous matches in scoring three goals, also went close with a shot which went narrowly over the bar.
When Podolski did find the net there looked no way back for Denmark but their response was as unexpected as it was impressive and they equalised five minutes later to send their fans, decked out in red and white, delirious.
Arsenal striker Nicklas Bendtner, who may well be pushed out of the north London club after they signed Podolski, won a header at the far post and the quick-thinking Krohn-Delhi flicked the ball past Manuel Neuer in a flash.
The Danes, who needed to win to go through, could have taken the lead in the 51st minute but Jakob Poulsen shaved the post from 10 metres after great set-up play from Bendtner.
With news of Portugal leading against the Dutch, a Denmark winner could have left three teams on six points but Germany left nothing to chance with Bender's late effort taking them into the quarter-finals with three group wins for the first time at the European Championship.
Krohn-Delhi, who also scored in Denmark's 1-0 win over the Netherlands, said his side could be proud of their performances.
"I am very disappointed like the rest of the team but I'm of course proud and I think we had something to offer," he said.
"We have a young team so we have a lot to work with."
